Question

How do you express `cos( (15 pi)/ 8 ) * cos (( pi) /3 )` without using products of trigonometric functions?

Answer 1

It is `cos(15pi/8)*cos(pi/3)=1/2[cos(5*pi/24)+cos(37/24*pi)]`

Explanation:

Well we know that

`cos(A+B)=cosA*cosB-sinA*sinB`

and

`cos(A-B)=cosA*cosB+sinA*sinB`

Add these two to get

`cosA*cosB=1/2[cos(A+B)+cos(A-B)]`

Hence for `A=15pi/8` and `B=pi/3` we have that

#cos(15pi/8)*cos(pi/3)=1/2[cos(15pi/8+pi/3)+cos(15pi/8-pi/3)]=> cos(15pi/8)*cos(pi/3)=1/2[cos(53/24*pi)+cos(37/24*pi)]=> cos(15pi/8)*cos(pi/3)=1/2[cos(5*pi/24)+cos(37/24*pi)]#